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                Department of Mathematical Sciences                       
                   The Johns Hopkins University                           
                                                                        
                              SEMINAR                                
                                                                        
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Shiyi Chen                                        November 2, 2000
Department of Mechanical Engineering              304 Whitehead Hall
The Johns Hopkins University                      NO PRESEMINAR
                                                  Refreshments: 3:30 p.m.
                                                  Seminar: 4:00 p.m.

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              KINETIC-BASED NUMERICAL METHODS FOR PDES

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                             ABSTRACT

The recent development of the lattice gas automata method and its extension
to the lattice Boltzmann method have provided new computational schemes for
solving a variety of partial differential equations and modeling different
physical systems.  The lattice methods, regarded as the simplest mesoscopic
and kinetic approaches which generate rich macroscopic dynamics, are fully
parallel and can, as a result, be easily programmed on parallel machines.
In this talk, we will introduce the basic principles of lattice gas and
lattice Boltzmann methods, their mathematical background, and numerical
implementations.  Comparisons of the lattice Boltzmann method with the
lattice gas technique and other traditional numerical schemes, including
finite difference schemes and pseudo-spectral methods, for solving the
Navier--Stokes equations will be discussed.  Recent achievements of the
lattice Boltzmann method and its applications in multiphase flows, flow
through porous media, MEMS, and fluid-particle interaction will be
presented.

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